Problem: $-ij - 8ik + 7i + 1 = 4j + 9$ Solve for $i$.
Answer: Combine constant terms on the right. $-ij - 8ik + 7i + {1} = 4j + {9}$ $-ij - 8ik + 7i = 4j + {8}$ Notice that all the terms on the left-hand side of the equation have $i$ in them. $-1{i}j - 8{i}k + 7{i} = 4j + 8$ Factor out the $i$ ${i} \cdot \left( -j - 8k + 7 \right) = 4j + 8$ Isolate the $i$ $i \cdot \left( -{j - 8k + 7} \right) = 4j + 8$ $i = \dfrac{ 4j + 8 }{ -{j - 8k + 7} }$